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2 years ago

Which shows the expression below in simplified form? (5 × 10^5) × (7 × 10^-5)

Mathematics

1 answer:

katrin [286]2 years ago

4 0

Answer:1,750,000,000

Step-by-step explanation:first the number ten to the fifth power is 1,000,000 then times five is 5,000,000. Then the number ten to the negative fifth power is 50 times seven is 350. 5,000,000 times 350 is 1,750,000,000

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the mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.5 %. assume

zhuklara [117]

Given:
Population proportion, $\mu _{p}$ = 57% = 0.57
Population standard deviation, σ = 3.5% = 0.035
Sample size, n = 40
Confidence level = 95%

The standard error is
$SE_{p} = \sqrt{ \frac{p(1-p)}{n} } = \sqrt{ \frac{0.57*0.43}{40} } =0.0783$

The confidence interval is
$\hat{p} \pm z^{*}SE_{p}$
where
$\hat{p}$ = sample proportion
z* = 1.96 at the 95% confidence lvvel

The sample proportion lies in the interval
(0.57-1.96*0.0783, 0.57+1.96*0.0783) = (0.4165, 0.7235)

Answer: Between 0.417 and 72.4), or between (41% and 72%)

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3 years ago

Write 3x^2-18x-6 in vertex form

Vedmedyk [2.9K]

The standard form of a quadratic equation is $\displaystyle{ y=ax^2+bx+c$ , while the vertex form is:

$y=a(x-h)^2+k$ , where (h, k) is the vertex of the parabola.

What we want is to write $\displaystyle{ y=3x^2-18x-6$ as $y=a(x-h)^2+k$

First, we note that all the three terms have a factor of 3, so we factorize it and write:

$\displaystyle{ y=3(x^2-6x-2)$ .

Second, we notice that $x^2-6x$ are the terms produced by $(x-3)^2=x^2-6x+9$ , without the 9. So we can write:

$x^2-6x=(x-3)^2-9$ , and substituting in $\displaystyle{ y=3(x^2-6x-2)$ we have:

$\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]$ .

Finally, distributing 3 over the two terms in the brackets we have:

$y=3[x-3]^2-33$ .

Answer: $y=3(x-3)^2-33$

6 0

2 years ago

Helpme Given f(x) = 3x - 1, find f(2). 1 2 5 4

dimulka [17.4K]

Answer:

Step-by-step explanation:

f(x)=3x-1

f(2)=3×2-1

f(2)=6-1

f(2)=5

7 0

2 years ago

Select all factors of the following polynomial:

Lena [83]

Step-by-step explanation:

4p³ + 36p² + 32p

= 4p(p² + 9p + 8)

= 4p(p + 1)(p + 8).

8 0

2 years ago

Write an inequality to match this statement: -7 is located to the right of -10. **Hint** You need to use shift and the comma but

vampirchik [111]

Answer:

-7 > -10

Step-by-step explanation:

We just have to compare these two numbers. When you're comparing two negative numbers, the smaller number is the bigger one. Ex. -3 is bigger than -6, so we can say that -3 > -6 (-3 is greater than -6). This means that -7 is larger than -10, which allows you to say that -7 > -10.

3 0

2 years ago